The most common and most likely answer to this crossword clue is the 8 letter word UNABATED
I've seen this crossword clue in Financial Times
U
N
A
B
A
T
E
D
More clues leading to the result UNABATED
- Relentless Danube flows over a treetop
- Persistent university fellow returned to host club
- Relentless girl hit newsman
- A French journalist covering a sports’ club is being relentless
- University academic leader upset about club that’s still going strong
- A bad tune played with no less energy
- Composed a bad tune with no let up
- A French journalist covering a sports club, being persistent
- Incessant university bar, upon retirement, spoiled date
- Ravishing beauty that's endless and intense
Buddy explains!

The straight part
We know that "Persistent" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case persistent = unabated.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does UNABATED mean?
UNABATED adjective- Continuing at full strength or intensity